---
slug: array-sort
title: array_sort lambda function
authors: [mbasmanova]
tags: [tech-blog,functions]
---

Presto provides an <a href="https://prestodb.io/docs/current/functions/array.html#array_sort">array_sort</a>
function to sort arrays in ascending order with nulls placed at the end.

```
presto> select array_sort(array[2, 5, null, 1, -1]);
        _col0
---------------------
 [-1, 1, 2, 5, null]
```

There is also an <a href="https://prestodb.io/docs/current/functions/array.html#array_sort_desc>">array_sort_desc</a>
function that sorts arrays in descending order with nulls placed at the end.

```
presto> select array_sort_desc(array[2, 5, null, 1, -1]);
        _col0
---------------------
 [5, 2, 1, -1, null]
```

Both array_sort and array_sort_desc place nulls at the end of the array.

There is also a version of <a href="https://prestodb.io/docs/current/functions/array.html#id2">array_sort</a>
function that takes a comparator lambda function and uses it to sort the array.

```
array_sort(array(T), function(T, T, int)) -> array(T)
```

A common use case is to sort an array of structs using one of the struct fields as the sorting key.

```
presto> select array_sort(array[row('apples', 23), row('bananas', 12), row('grapes', 44)],
        -> (x, y) -> if (x[2] < y[2], -1, if(x[2] > y[2], 1, 0)));

                                         _col0
---------------------------------------------------------------------------------------
 [{f0=bananas, f1=12}, {f0=apples, f1=23}, {f0=grapes, f1=44}]
```

This is all very nice and convenient, but there is a catch.

The documentation says that the "comparator will take two nullable arguments representing two
nullable elements of the array."" Did you notice the word "nullable" in "nullable arguments"
and "nullable elements"? Do you think it is important? It is Ok if the answer is No or Not Really.
Turns out this "nullable" thing is very important. The comparator is expected to handle null
inputs and should not assume that inputs are not null or that nulls are handled automatically.

Why is it important to handle null inputs? Let’s see what happens if the comparator doesn’t
handle nulls.

```
presto> select array_sort(array[2, 3, null, 1],
                            (x, y) -> if (x < y, -1, if (x > y, 1, 0)));
      _col0
-----------------
 [2, 3, null, 1]
```

The result array is not sorted! If subsequent logic relies on the array to be sorted the query
will silently return wrong results. And if there is no logic that relies on the sortedness of
the array then why waste CPU cycles on sorting?

Why is the array not sorted? That’s because the comparator returns 0 whenever x or y is null.

```
	x < y  returns null if x or y is null, then
	x > y  returns null if x or y is null, then
	result is 0
```

This confuses the sorting algorithm as it sees that 1 == null, 2 == null, 3 == null,
but 1 != 2 and 1 != 3. The algorithm assumes that the comparator function is written correctly,
e.g. if a < b then b > a and if a == b and b == c then a == c. Comparator function that doesn’t
handle nulls does not satisfy these rules and causes unpredictable results.

To handle null inputs, the comparator function needs to be modified, for example, like so:

```
	(x, y) -> CASE WHEN x IS NULL THEN 1
								WHEN y IS NULL THEN -1
								WHEN x < y THEN -1
								WHEN x > y THEN 1
								ELSE 0 END
```

```
presto> select array_sort(array[2, 3, null, 1],
        -> (x, y) -> CASE WHEN x IS NULL THEN 1
        -> WHEN y IS NULL THEN -1
        -> WHEN x < y THEN -1
        -> WHEN x > y THEN 1
        -> ELSE 0 END
        -> );
      _col0
-----------------
 [1, 2, 3, null]
```

This is longer and harder to read, but the result array is sorted properly. The new
comparator says that null is greater than any other value, so null is placed at the
end of the array.

Note: When (x, y) return -1, the algorithm assumes that x \<= y.


Writing comparators correctly is not easy. Writing comparators that handle null inputs
is even harder. Having no feedback when a comparator is written incorrectly makes it
yet harder to spot bugs and fix them before a query lands in production and starts
producing wrong results.

I feel that Presto’s array_sort function with a custom comparator is dangerous and hard
to use and I wonder if it makes sense to replace it with a safer, easier to use alternative.

```
array_sort(array(T), function(T, U)) -> array(T)
```

This version takes an array and a transform lambda function that specifies how to compute
sorting keys from the array elements.

To sort array of structs by one of the struct fields, one would write

```
presto> select array_sort(array[row('apples', 23), row('bananas', 12), row('grapes', 44)],
                            x -> x[2])

                                         _col0
---------------------------------------------------------------------------------------
 [{f0=bananas, f1=12}, {f0=apples, f1=23}, {f0=grapes, f1=44}]
```

This version would sort the array by the sorting keys computed using the specified lambda
in ascending order placing nulls at the end of the array.

A matching array_sort_desc function would sort in descending order placing nulls at the end
of the array.

These functions would be easier to write and read and null handling will happen automatically.

We implemented these functions in <a href="https://facebookincubator.github.io/velox/functions/presto/array.html#id0">Velox</a>.


We also added partial support for array_sort with a comparator lambda function. Expression
compiler in Velox analyzes the comparator expression to determine whether it can be re-written
to the alternative version of array_sort. If so, it re-writes the expression and evaluates it.
Otherwise, it throws an unsupported exception.

For example,

```
	array_sort(a, (x, y) -> if (x[2] < y[2], -1, if(x[2] > y[2], 1, 0)))
```

is re-written to

```
	array_sort(a, x -> x[2])
```

This rewrite allows Prestissimo and Presto-on-Spark-on-Velox to support common use cases
and do so efficiently.

The rewrite handles a few different ways to express the same comparator. Some examples:

```
    // becomes array_sort(a, f(x))
	(x, y) -> if(f(x) < f(y), -1, if(f(x) > f(y), 1, 0))

	// becomes array_sort_desc(a, f(x))
	(x, y) -> if(f(x) < f(y), 1, if(f(x) > f(y), -1, 0))

	// becomes array_sort(a, f(x))
	(x, y) -> if(f(x) < f(y), -1, if(f(x) = f(y), 0, 1))

	// becomes array_sort(a, f(x))
	(x, y) -> if(f(x) = f(y), 0, if(f(x) < f(y), -1, 1))

	// becomes array_sort(a, f(x))
	(x, y) -> if(f(y) < f(x), 1, if(f(x) < f(y), -1, 0))
```

Why didn’t we implement full support for comparator lambda functions in array_sort? Actually,
we couldn’t think of an efficient way to do that in a vectorized engine. Velox doesn’t use code
generation and interprets expressions. It can do that efficiently if it can process data in large
batches. array_sort with custom comparator doesn’t lend itself well to such processing.

array_sort with a transform lambda works well in a vectorized engine. To process a batch of arrays,
Velox first evaluates the transform lambda on all the elements of the arrays, then sorts the results.


For further reading, consider the <a href="https://opensource.googleblog.com/2022/06/Vectorized%20and%20performance%20portable%20Quicksort.html">Vectorized and performance-portable Quicksort</a>
blog post from Google.

Thank you <a href="https://www.linkedin.com/in/orrierling">Orri Erling</a> for brainstorming
and <a href="https://www.linkedin.com/in/xiaoxuanmeng">Xiaoxuan Meng</a> for reviewing the code.
